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4MA1/1F Jun 2018, Question 12: Describing Transformations

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1F (Foundation) · Calculator · 4 marks

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The question, in short

Using the grid with triangles A and B, identify the single transformation linking A to B, draw B moved by vector (2, −6) as C, then state the single transformation taking C back to B.

Summarised in our own words. Use the official paper for the exact wording and the diagram.

Part (a) · 2 marks

State the one transformation, with all details, that carries triangle A onto triangle B.

  1. 1Triangle A and triangle B are mirror images across the vertical line x = −1.
  2. 2The line x = −1 is the perpendicular bisector of the segments joining corresponding vertices of triangles A and B.
  3. 3This transformation is a reflection in the line x = −1.

AnswerReflection in x = −1

Part (b) · 1 mark

Draw triangle C on the grid by shifting triangle B using the vector (2, −6).

  1. 1The vector means move 2 to the right and 6 down
  2. 2Triangle B has vertices (1, 5), (1, 1) and (3, 1)
  3. 3(1, 5) → (1 + 2, 5 − 6) = (3, −1)
  4. 4(1, 1) → (1 + 2, 1 − 6) = (3, −5)
  5. 5(3, 1) → (3 + 2, 1 − 6) = (5, −5)
  6. 6Draw the triangle with vertices (3, −1), (3, −5), (5, −5) and label it C

Answer(3, −1) (3, −5) (5, −5)

Part (c) · 1 mark

Give the single transformation, fully described, that carries triangle C onto triangle B.

  1. 1Triangle C was obtained from triangle B by moving 2 right and 6 down
  2. 2To map C back onto B, reverse that movement
  3. 3Move 2 to the left and 6 up
  4. 4So the single transformation is a translation by the column vector (−2, 6)

AnswerTranslation by the column vector (−2, 6), i.e. 2 left and 6 up

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